An aspect of secession, as illustrated in more depth here: https://en.wikipedia.org/wiki/Secession is identified by the adjective formal - “The act of secession is the formal withdrawal from a union or confederation”.
As in a circumstance such as divorce there is mutuality of terms and purpose between all parties. If you look at the examples at the link you see references to ratifications and negotiated consent.
My point is that there was none of that with the colonialist rebels. It was actually more than just an announcement - it was a throwing down the gauntlet in full recognition of the likely response.
We didn’t simply “withdraw” from British rule - we tore ourselves away from their control. We didn’t secede against their authority - we openly rebelled against it. We didn’t give a damn if they liked it or not - we were beyond “praying for relief” or asking for consideration.
Whatever.
Anyway, “secession” is a legal term of art which legal definition as cited in Black’s Legal Dictionary is the generally accepted definition in the legal profession, not subject to your or Wikipedia’s definition.
Bye.
From the June 29, 1776, Virginia Constitution (Link) which listed grievances against the rule of George III and then declared (red bold emphasis mine):
"By which acts of misrule, the government of this country, as formerly exercised by the Crown of Great Britain, is TOTALLY DISSOLVED."
Is that formal enough for you? Note that the United States was not mentioned.
Consider South Carolina's Ordinance of Secession (Link2):
AN ORDINANCE to dissolve the union between the State of South Carolina and other States united with her under the compact entitled "The Constitution of the United States of America."
Sound similar to the 1776 Virginia dissolution? From the Wikipedia link you provided: "Secession (derived from the Latin term secessio) is the withdrawal of a group from a larger entity, especially a political entity (a country), but also any organization, union or military alliance.